We present a numerical study of anisotropic statistical fluctuations in homogeneous turbulent flows. We give a new argument to predict the dimensional scaling exponents, ${\zeta }_d^j\mathrm{}\left(p\right)=(p+j)/3,$ for the projections of the $p$th order structure function in the $j$th sector of the rotational group. We show that the measured exponents are anomalous, showing a clear deviation from the dimensional prediction. Dimensional scaling is subleading and connected to the dynamical fluctuations without phase correlations. Universality of the observed anomalous scaling is discussed both theoretically and by means of numerical simulations at different Reynolds numbers and with different forcing.

• Received 6 March 2002

DOI:https://doi.org/10.1103/PhysRevE.66.056306